{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 2\n",
    "## 问题描述\n",
    "对附件Data2.xls中的数据，建立颜色读数和物质浓度的数学模型，并给出模型的误差分析。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import pandas as pd \n",
    "from matplotlib import pyplot as plt \n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   substance  ppm    R    G    B    S    H\n0       SO_2    0  153  148  157  138   14\n1       SO_2    0  153  147  157  138   16\n2       SO_2    0  153  146  158  137   20\n3       SO_2    0  153  146  158  137   20\n4       SO_2    0  154  145  157  141   19\n5       SO_2   20  144  115  170  135   82\n6       SO_2   20  144  115  169  136   81\n7       SO_2   20  145  115  172  135   83\n8       SO_2   30  145  114  174  135   87\n9       SO_2   30  145  114  176  135   89\n10      SO_2   30  145  114  175  135   89\n11      SO_2   30  146  114  175  135   88\n12      SO_2   50  142   99  175  137  110\n13      SO_2   50  141   99  174  137  109\n14      SO_2   50  142   99  176  136  110\n15      SO_2   80  141   96  181  135  119\n16      SO_2   80  141   96  182  135  119\n17      SO_2   80  140   96  182  135  120\n18      SO_2  100  139   96  175  136  115\n19      SO_2  100  139   96  174  136  114\n20      SO_2  100  139   96  176  136  116\n21      SO_2  150  139   86  178  136  131\n22      SO_2  150  139   87  177  137  129\n23      SO_2  150  138   86  177  137  130\n24      SO_2  150  139   86  178  137  131",
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<td>146</td>\n      <td>158</td>\n      <td>137</td>\n      <td>20</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>SO_2</td>\n      <td>0</td>\n      <td>153</td>\n      <td>146</td>\n      <td>158</td>\n      <td>137</td>\n      <td>20</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>SO_2</td>\n      <td>0</td>\n      <td>154</td>\n      <td>145</td>\n      <td>157</td>\n      <td>141</td>\n      <td>19</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>SO_2</td>\n      <td>20</td>\n      <td>144</td>\n      <td>115</td>\n      <td>170</td>\n      <td>135</td>\n      <td>82</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>SO_2</td>\n      <td>20</td>\n      <td>144</td>\n      <td>115</td>\n      <td>169</td>\n      <td>136</td>\n      <td>81</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>SO_2</td>\n      <td>20</td>\n      <td>145</td>\n      <td>115</td>\n      <td>172</td>\n      <td>135</td>\n      <td>83</td>\n    </tr>\n    <tr>\n      <th>8</th>\n 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<td>100</td>\n      <td>139</td>\n      <td>96</td>\n      <td>174</td>\n      <td>136</td>\n      <td>114</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>SO_2</td>\n      <td>100</td>\n      <td>139</td>\n      <td>96</td>\n      <td>176</td>\n      <td>136</td>\n      <td>116</td>\n    </tr>\n    <tr>\n      <th>21</th>\n      <td>SO_2</td>\n      <td>150</td>\n      <td>139</td>\n      <td>86</td>\n      <td>178</td>\n      <td>136</td>\n      <td>131</td>\n    </tr>\n    <tr>\n      <th>22</th>\n      <td>SO_2</td>\n      <td>150</td>\n      <td>139</td>\n      <td>87</td>\n      <td>177</td>\n      <td>137</td>\n      <td>129</td>\n    </tr>\n    <tr>\n      <th>23</th>\n      <td>SO_2</td>\n      <td>150</td>\n      <td>138</td>\n      <td>86</td>\n      <td>177</td>\n      <td>137</td>\n      <td>130</td>\n    </tr>\n    <tr>\n      <th>24</th>\n      <td>SO_2</td>\n      <td>150</td>\n      <td>139</td>\n      <td>86</td>\n      <td>178</td>\n      <td>137</td>\n      <td>131</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "source": [
    "data2 = pd.read_excel('Data2.xls')\n",
    "data2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 思路一：函数模型拟合\n",
    "使用scipy.optimize.curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[array([1.40686427e+01, 3.29488773e-02, 1.38910437e+02]),\n array([5.65247131e+01, 3.13425489e-02, 8.92339517e+01]),\n array([ -18.4       , 1126.66061306,  175.8       ]),\n array([  2.4,   1. , 135.8]),\n array([-1.06189205e+02,  3.88749250e-02,  1.24730556e+02])]"
     },
     "metadata": {},
     "execution_count": 15
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "poptlist = []\n",
    "def curve_model(x,a,b,c):\n",
    "    return a*np.exp(-b*x)+c\n",
    "for i,(color_index,color) in enumerate(zip('RGBSH',('r','g','brown','purple','orange'))):\n",
    "    plt.subplot(int(f'23{i+1}'))\n",
    "    plt.scatter(data2['ppm'],data2[color_index],c=color)\n",
    "    popt,pcov = curve_fit(curve_model,data2['ppm'],data2[color_index])\n",
    "    x = np.linspace(0,150,150)\n",
    "    plt.plot(x,curve_model(x,*popt))\n",
    "    poptlist.append(popt)\n",
    "    # plt.title(f'SO_2-{color_index}')\n",
    "poptlist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 思路二：使用神经网路"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.neural_network import MLPRegressor\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x_data_0 = data2[list('RGBSH')]\n",
    "x_data_scaler = StandardScaler().fit(x_data_0)\n",
    "x_data_1 = x_data_scaler.transform(x_data_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_data_0 = np.array(data2['ppm']).reshape(-1,1)\n",
    "y_data_scaler = StandardScaler().fit(y_data_0)\n",
    "y_data_1 = y_data_scaler.transform(y_data_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([  0. ,   0. ,   0.2,   0.2,   0. ,  20.6,  20.8,  21.3,  30.4,\n        30.6,  30.6,  30.6,  51.8,  58.8,  49.6,  78.1,  78.1,  85. ,\n        99.3,  99.3,  99.8, 141.7, 148.8, 148.8, 148.8])"
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "source": [
    "rfr = RandomForestRegressor()\n",
    "rfr.fit(x_data_0,y_data_0)\n",
    "rfr.score(x_data_0,y_data_0)\n",
    "rfr.predict(x_data_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "MLPRegressor(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,\n             beta_2=0.999, early_stopping=False, epsilon=1e-08,\n             hidden_layer_sizes=[8, 20, 20, 8], learning_rate='constant',\n             learning_rate_init=0.001, max_fun=15000, max_iter=1000,\n             momentum=0.9, n_iter_no_change=10, nesterovs_momentum=True,\n             power_t=0.5, random_state=None, shuffle=True, solver='adam',\n             tol=0.0001, validation_fraction=0.1, verbose=False,\n             warm_start=False)"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "regressor = MLPRegressor([8,20,20,8],max_iter=1000) \n",
    "regressor.fit(x_data_1,y_data_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.9899165185673198"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "regressor.score(x_data_1,y_data_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(array([ -1.61122867,  -1.15912341,   1.50048224,   1.50048224,\n         -5.89333183,  30.82581265,  30.11901702,  31.22141043,\n         32.36189999,  34.80536742,  33.92509217,  32.27217019,\n         49.43310936,  56.18682714,  53.23118094,  76.41982719,\n         74.05443539,  84.71265051, 102.28343243, 101.31628611,\n        102.16104416, 147.13380859, 144.01722039, 155.55732119,\n        146.50410784]),\n array([[  0],\n        [  0],\n        [  0],\n        [  0],\n        [  0],\n        [ 20],\n        [ 20],\n        [ 20],\n        [ 30],\n        [ 30],\n        [ 30],\n        [ 30],\n        [ 50],\n        [ 50],\n        [ 50],\n        [ 80],\n        [ 80],\n        [ 80],\n        [100],\n        [100],\n        [100],\n        [150],\n        [150],\n        [150],\n        [150]], dtype=int64))"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "y_predict_1 = regressor.predict(x_data_1)\n",
    "y_predict_0 = y_data_scaler.inverse_transform(y_predict_1)\n",
    "y_predict_0,y_data_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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